Re: Where is Truth?
machine
in a quasi-direct way. The second, the physical one, result from very
deep long and competitive struggle between all universal machines.
Would you restrict (your) machine to structural components within
our inventory of today?
Not at all. They can have many clothes, and many different type of
relative clothes.
HER functions to restricted into OUR present sortiment of
activities? I like to call it an ORGANIZATION and no such
restriction emerge. It is only a name. WE are orgqnizations as
well, with unlimited (into our models that is) connections into the
WORLD (infinite complexity of everything). Your Universal Computer
may be even more compact and outreaching. (I am not talking about
our present binary embryonic digital Kraxlwerks - we call our
computers).
*Assuming* yes doctor, you and me are such universal machine, but
here you and me does not refer to our special earth-local
incarnation, but all the arithmetical incarnations.
Thanks for your thoughts
With pleasure,
Best,
Bruno
On Sat, Oct 22, 2011 at 9:26 AM, Bruno Marchal marc...@ulb.ac.be
wrote:
On 21 Oct 2011, at 22:09, John Mikes wrote:
Hi Stephen,
it seems you are closing to 'my alley'.
First: if you don't think of T R U T H (in any absolute sense,
meaning it's acceptable 'meaning') how can you abide by a version
of it? - What are the REALS?
I do not consider 'Arithmetic' the one and only ontological
primitive: I cannot 'see' ontology at all in a world that changes
ceaselessly and the 'being' (ontology) turns into 'becoming' (sort
of epistemology?) with changing away at the instant you would
realize it became.
Idem per idem is not a workable position. You can explain a
'system' only in terms looking at it from a different (outside?)
view. Platonism is such a system. I try a common sense platform.
I asked Bruno several times how he explains as the abstract
'numbers' (not the markers of quantity, mind you) which makes the
fundamentals of the world. He explained: arithmetically 2 lines
(II) and 3 lines (III) making 5 (I) that is indeed viewable
exactly as quantity-markers (of lines or whatever).
That's the idea.
Of course a zero (no lines) would introduce the SPACE between lines
- yet another quantity, so with the 'abstract' of numbers we got
bugged down in measurement techniques (physics?).
Here you might be too much literal already. The numbers are more of
the type of mind ability to distinguish quantities of similar
things. It is more in the mind, than in the way we might use a local
reality to describe them.
Logic? a human way of thinking (cf the Zarathustrans in the Cohen-
Stewart books Collapse of Chaos and The Figment of Reality) with
other (undefinable and unlimited) ways available (maybe) in the
'infinite complexity' of the world
- IF our term of a 'logic' is realizable in it at all.
If logic is a human way of thinking, is not logics ways of thinking
(note the plural). There are infinities of logic. Classical logic is
the way of the greek human thinking, and of the he ideally
arithmetically correct machine, which can be studied to learn about
us, like the bacteria Escherichia coli can studied for learning
something about us.
You know a lot more in math-related terms than I do, so I gave only
the tips of my icebergs in my thinking.
Then there is my agnosticism: the belief in the unknown part of the
world that yet influences whatever we think of.
But here is the problem: what do you mean by world? Is there a
world? Why not a dream. If you agree that there is something
unknown, you believe that there is something to be known or believed
OK?
We continually learn further parts of it, but only to the extent of
the capabilities of our (restricted) mental capacity. So whatever
we 'know' is partial and inadequate (adjuste, incomplete) into our
'mini-solipsism' of Colin Hales.
What is the difference with the first person's beliefs? And with the
first person knowledge. Are you OK with the idea that a machine can
also have her mini-solipsism? (this would not imply that we are
machine, just that a machine could think). I just try to have a more
precise idea of your thinking.
Best,
Bruno
Regards
John M
On Fri, Oct 21, 2011 at 7:07 AM, Stephen P. King stephe...@charter.net
wrote:
Hi John,
I was not thinking of truth in any absolute sense. I'm not even
sure what that concept means... I was just considering the
definiteness of the so-called truth value that one associates with
Boolean logic, as in it has a range {0,1). There are logics where
this can vary over the Reals!
My question is about where does arithmetical truth get coded
given that it cannot be defined in arithmetic itself? If we
consider Arithmetic to be the one and only ontological primitive,
it seems to me that we lose the ability to define the very
meaningfulness of arithmetic
Re: Where is Truth?
On 21 Oct 2011, at 22:09, John Mikes wrote:
Hi Stephen,
it seems you are closing to 'my alley'.
First: if you don't think of T R U T H (in any absolute sense,
meaning it's acceptable 'meaning') how can you abide by a version of
it? - What are the REALS?
I do not consider 'Arithmetic' the one and only ontological
primitive: I cannot 'see' ontology at all in a world that changes
ceaselessly and the 'being' (ontology) turns into 'becoming' (sort
of epistemology?) with changing away at the instant you would
realize it became.
Idem per idem is not a workable position. You can explain a
'system' only in terms looking at it from a different (outside?)
view. Platonism is such a system. I try a common sense platform.
I asked Bruno several times how he explains as the abstract
'numbers' (not the markers of quantity, mind you) which makes the
fundamentals of the world. He explained: arithmetically 2 lines (II)
and 3 lines (III) making 5 (I) that is indeed viewable exactly
as quantity-markers (of lines or whatever).
That's the idea.
Of course a zero (no lines) would introduce the SPACE between lines
- yet another quantity, so with the 'abstract' of numbers we got
bugged down in measurement techniques (physics?).
Here you might be too much literal already. The numbers are more of
the type of mind ability to distinguish quantities of similar things.
It is more in the mind, than in the way we might use a local reality
to describe them.
Logic? a human way of thinking (cf the Zarathustrans in the Cohen-
Stewart books Collapse of Chaos and The Figment of Reality) with
other (undefinable and unlimited) ways available (maybe) in the
'infinite complexity' of the world
- IF our term of a 'logic' is realizable in it at all.
If logic is a human way of thinking, is not logics ways of thinking
(note the plural). There are infinities of logic. Classical logic is
the way of the greek human thinking, and of the he ideally
arithmetically correct machine, which can be studied to learn about
us, like the bacteria Escherichia coli can studied for learning
something about us.
You know a lot more in math-related terms than I do, so I gave only
the tips of my icebergs in my thinking.
Then there is my agnosticism: the belief in the unknown part of the
world that yet influences whatever we think of.
But here is the problem: what do you mean by world? Is there a
world? Why not a dream. If you agree that there is something unknown,
you believe that there is something to be known or believed OK?
We continually learn further parts of it, but only to the extent of
the capabilities of our (restricted) mental capacity. So whatever we
'know' is partial and inadequate (adjuste, incomplete) into our
'mini-solipsism' of Colin Hales.
What is the difference with the first person's beliefs? And with the
first person knowledge. Are you OK with the idea that a machine can
also have her mini-solipsism? (this would not imply that we are
machine, just that a machine could think). I just try to have a more
precise idea of your thinking.
Best,
Bruno
Regards
John M
On Fri, Oct 21, 2011 at 7:07 AM, Stephen P. King stephe...@charter.net
wrote:
Hi John,
I was not thinking of truth in any absolute sense. I'm not even
sure what that concept means... I was just considering the
definiteness of the so-called truth value that one associates with
Boolean logic, as in it has a range {0,1). There are logics where
this can vary over the Reals!
My question is about where does arithmetical truth get coded
given that it cannot be defined in arithmetic itself? If we consider
Arithmetic to be the one and only ontological primitive, it seems to
me that we lose the ability to define the very meaningfulness of
arithmetic! This is a very different thing than coding one
arithmetic statement in another, as we have with Goedel numbering.
What I am pointing out is that if we are beign consisstent we have
to drop the presumption of an entity to whom a problem is defined,
i.e. valuated. This is the problem that I have with all forms of
Platonism, they assume something that they disallow: an entity to
whom meaning is definite. What distinguishes the Forms from each
other at the level of the Forms?
Onward!
Stephen
On 10/20/2011 10:18 PM, John Mikes wrote:
Dear Stephen,
as long as we are not omniscient (good condition for
impossibillity) there is no TRUTH. As Bruno formulates his reply:
there is something like mathematical truth - but did you ask for
such specififc definition?
Now - about mathematical truth? new funamental inventions in math
(even maybe in arithmetics Bruno?) may alter the ideas that were
considered as mathematical truth before those inventions. Example:
the zero etc.
It always depends on the context one looks at the problem FROM and
draws conclusion INTO.
John M
On Sun, Oct 16, 2011
Re: Where is Truth?
icebergs in my thinking. *
**
*Then there is my agnosticism: the belief in the unknown part of the world
that yet influences whatever we think of. *
But here is the problem: what do you mean by world? Is there a world? Why
not a dream. If you agree that there is something unknown, you believe that
there is something to be known or believed OK?
*We continually learn further parts of it, but only to the extent of the
capabilities of our (restricted) mental capacity. So whatever we 'know' is
partial and inadequate (adjuste, incomplete) into our 'mini-solipsism' of
Colin Hales. *
What is the difference with the first person's beliefs? And with the first
person knowledge. Are you OK with the idea that a machine can also have her
mini-solipsism? (this would not imply that we are machine, just that a
machine could think). I just try to have a more precise idea of your
thinking.
Best,
Bruno
**
*Regards*
**
*John M*
**
**
* *
On Fri, Oct 21, 2011 at 7:07 AM, Stephen P. King stephe...@charter.netwrote:
Hi John,
I was not thinking of truth in any absolute sense. I'm not even sure
what that concept means... I was just considering the definiteness of the
so-called truth value that one associates with Boolean logic, as in it has a
range {0,1). There are logics where this can vary over the Reals!
My question is about where does arithmetical truth get coded given
that it cannot be defined in arithmetic itself? If we consider Arithmetic to
be the one and only ontological primitive, it seems to me that we lose the
ability to define the very meaningfulness of arithmetic! This is a very
different thing than coding one arithmetic statement in another, as we have
with Goedel numbering. What I am pointing out is that if we are beign
consisstent we have to drop the presumption of an entity to whom a problem
is defined, i.e. valuated. This is the problem that I have with all forms of
Platonism, they assume something that they disallow: an entity to whom
meaning is definite. What distinguishes the Forms from each other at the
level of the Forms?
Onward!
Stephen
On 10/20/2011 10:18 PM, John Mikes wrote:
Dear Stephen,
as long as we are not omniscient (good condition for impossibillity) there
is no TRUTH. As Bruno formulates his reply:
there is something like mathematical truth - but did you ask for such
specififc definition?
Now - about mathematical truth? new funamental inventions in math (even
maybe in arithmetics Bruno?) may alter the ideas that were considered as
mathematical truth before those inventions. Example: the zero etc.
It always depends on the context one looks at the problem FROM and draws
conclusion INTO.
John M
On Sun, Oct 16, 2011 at 12:48 AM, Stephen P. King
stephe...@charter.netwrote:
Hi,
I ran across the following:
http://en.wikipedia.org/wiki/Tarski%27s_indefinability_theorem
*Tarski's undefinability theorem*, stated and proved by Alfred
Tarskihttp://en.wikipedia.org/wiki/Alfred_Tarskiin 1936, is an important
limitative result in mathematical
logic http://en.wikipedia.org/wiki/Mathematical_logic, the foundations
of mathematics http://en.wikipedia.org/wiki/Foundations_of_mathematics,
and in formal semantics http://en.wikipedia.org/wiki/Semantics.
Informally, the theorem states that *arithmetical truth cannot be
defined in arithmetic*.
Where then is it defined?
Onward!
Stephen
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Re: Where is Truth?
Hi John,
I was not thinking of truth in any absolute sense. I'm not even
sure what that concept means... I was just considering the definiteness
of the so-called truth value that one associates with Boolean logic, as
in it has a range {0,1). There are logics where this can vary over the
Reals!
My question is about where does arithmetical truth get coded
given that it cannot be defined in arithmetic itself? If we consider
Arithmetic to be the one and only ontological primitive, it seems to me
that we lose the ability to define the very meaningfulness of
arithmetic! This is a very different thing than coding one arithmetic
statement in another, as we have with Goedel numbering. What I am
pointing out is that if we are beign consisstent we have to drop the
presumption of an entity to whom a problem is defined, i.e. valuated.
This is the problem that I have with all forms of Platonism, they assume
something that they disallow: an entity to whom meaning is definite.
What distinguishes the Forms from each other at the level of the Forms?
Onward!
Stephen
On 10/20/2011 10:18 PM, John Mikes wrote:
Dear Stephen,
as long as we are not omniscient (good condition for impossibillity)
there is no TRUTH. As Bruno formulates his reply:
there is something like mathematical truth - but did you ask for
such specififc definition?
Now - about mathematical truth? new funamental inventions in math
(even maybe in arithmetics Bruno?) may alter the ideas that were
considered as mathematical truth before those inventions. Example: the
zero etc.
It always depends on the context one looks at the problem FROM and
draws conclusion INTO.
John M
On Sun, Oct 16, 2011 at 12:48 AM, Stephen P. King
stephe...@charter.net mailto:stephe...@charter.net wrote:
Hi,
I ran across the following:
http://en.wikipedia.org/wiki/Tarski%27s_indefinability_theorem
*Tarski's undefinability theorem*, stated and proved by Alfred
Tarski http://en.wikipedia.org/wiki/Alfred_Tarski in 1936, is an
important limitative result in mathematical logic
http://en.wikipedia.org/wiki/Mathematical_logic, the foundations
of mathematics
http://en.wikipedia.org/wiki/Foundations_of_mathematics, and in
formal semantics http://en.wikipedia.org/wiki/Semantics.
Informally, the theorem states that /arithmetical truth cannot be
defined in arithmetic/.
Where then is it defined?
Onward!
Stephen
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Re: Where is Truth?
is
endless! But there does seem to be a pattern to this madness! It seems
as if for every kind of set there is a logic having its own algebra and
isomorphic to some topological space. So this 4-ality is just another
communicable idea.
**
*You know a lot more in math-related terms than I do, so I gave only
the tips of my icebergs in my thinking. *
I have spent the last 20 years studying philosophy, physics and
mathematics on my own and discussing ideas with many people. I have no
one to blame for my strange ideas except myself. ;-) If they make some
sense to someone other than me, that is wonderful, as sometimes I do not
even understand my own mussing! It is I get possessed. It may just be
madness. ;-P
**
*Then there is my agnosticism: the belief in the unknown part of the
world that yet influences whatever we think of. We continually learn
further parts of it, but only to the extent of the capabilities of our
(restricted) mental capacity. So whatever we 'know' is partial and
inadequate (adjuste, incomplete) into our 'mini-solipsism' of Colin
Hales. *
I have a similar belief, I try not to name it because to do so
constrains it to be one thing and nothing else! ;-)
Onward!
Stephen
**
*Regards*
**
*John M*
**
**
**
On Fri, Oct 21, 2011 at 7:07 AM, Stephen P. King
stephe...@charter.net mailto:stephe...@charter.net wrote:
Hi John,
I was not thinking of truth in any absolute sense. I'm not
even sure what that concept means... I was just considering the
definiteness of the so-called truth value that one associates with
Boolean logic, as in it has a range {0,1). There are logics where
this can vary over the Reals!
My question is about where does arithmetical truth get coded
given that it cannot be defined in arithmetic itself? If we
consider Arithmetic to be the one and only ontological primitive,
it seems to me that we lose the ability to define the very
meaningfulness of arithmetic! This is a very different thing than
coding one arithmetic statement in another, as we have with Goedel
numbering. What I am pointing out is that if we are beign
consisstent we have to drop the presumption of an entity to whom a
problem is defined, i.e. valuated. This is the problem that I have
with all forms of Platonism, they assume something that they
disallow: an entity to whom meaning is definite. What
distinguishes the Forms from each other at the level of the Forms?
Onward!
Stephen
On 10/20/2011 10:18 PM, John Mikes wrote:
Dear Stephen,
as long as we are not omniscient (good condition for
impossibillity) there is no TRUTH. As Bruno formulates his reply:
there is something like mathematical truth - but did you ask
for such specififc definition?
Now - about mathematical truth? new funamental inventions in math
(even maybe in arithmetics Bruno?) may alter the ideas that were
considered as mathematical truth before those inventions.
Example: the zero etc.
It always depends on the context one looks at the problem FROM
and draws conclusion INTO.
John M
On Sun, Oct 16, 2011 at 12:48 AM, Stephen P. King
stephe...@charter.net mailto:stephe...@charter.net wrote:
Hi,
I ran across the following:
http://en.wikipedia.org/wiki/Tarski%27s_indefinability_theorem
*Tarski's undefinability theorem*, stated and proved by
Alfred Tarski http://en.wikipedia.org/wiki/Alfred_Tarski in
1936, is an important limitative result in mathematical logic
http://en.wikipedia.org/wiki/Mathematical_logic, the
foundations of mathematics
http://en.wikipedia.org/wiki/Foundations_of_mathematics,
and in formal semantics
http://en.wikipedia.org/wiki/Semantics. Informally, the
theorem states that /arithmetical truth cannot be defined in
arithmetic/.
Where then is it defined?
Onward!
Stephen
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Re: Where is Truth?
Dear Stephen, as long as we are not omniscient (good condition for impossibillity) there is no TRUTH. As Bruno formulates his reply: there is something like mathematical truth - but did you ask for such specififc definition? Now - about mathematical truth? new funamental inventions in math (even maybe in arithmetics Bruno?) may alter the ideas that were considered as mathematical truth before those inventions. Example: the zero etc. It always depends on the context one looks at the problem FROM and draws conclusion INTO. John M On Sun, Oct 16, 2011 at 12:48 AM, Stephen P. King stephe...@charter.netwrote: Hi, I ran across the following: http://en.wikipedia.org/wiki/Tarski%27s_indefinability_theorem *Tarski's undefinability theorem*, stated and proved by Alfred Tarskihttp://en.wikipedia.org/wiki/Alfred_Tarskiin 1936, is an important limitative result in mathematical logic http://en.wikipedia.org/wiki/Mathematical_logic, the foundations of mathematics http://en.wikipedia.org/wiki/Foundations_of_mathematics, and in formal semantics http://en.wikipedia.org/wiki/Semantics. Informally, the theorem states that *arithmetical truth cannot be defined in arithmetic*. Where then is it defined? Onward! Stephen -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Where is Truth?
On 16 Oct 2011, at 06:48, Stephen P. King wrote: Hi, I ran across the following: http://en.wikipedia.org/wiki/Tarski%27s_indefinability_theorem Tarski's undefinability theorem, stated and proved by Alfred Tarski in 1936, is an important limitative result in mathematical logic, the foundations of mathematics, and in formal semantics. Informally, the theorem states that arithmetical truth cannot be defined in arithmetic. Where then is it defined? You can defined arithmetical truth in second order arithmetic; or in set theory. I have often mentioned Tarski non definability of truth to explain that a machine cannot define its own knowledge notion, including in sane04 and almost all the papers of mine that I cite. We cannot define Kp by Bp True(p) because the machine cannot define, in its own language True(p). By the diagonalization lemma we would be able to construct Epimenides' paradoxical I am not true sentence. It might be possible to define knowledge (S4 modal operator) in some other way, but this has been shown impossible to by Kaplan Montague. Of course Gödel knew that Bp cannot be a knowledge operator. Amazingly it acts like a belief operator, confirming that the ideal science of the correct machine leads only to beliefs (roughly speaking). But we can define a knowledge operator at the metalevel, and this in the Theaetetus modus operandi, just by modeling the truth of an arithmetical proposition p by itself. This is the origin of the Bp p hypostase. It works fine and lead to the S4Grz logic. Also, I have often mentioned that, although a machine cannot compute nor even defined all its theology (the 8 hypostases), a rich Löbian machine, like ZF can define and study the whole theology of a simpler Löbian machine. Then, the rich LUM can lift that theology on itself, by betting on its own correctness, but at his own risk and peril: such an operation should not lead the machine to use its correctness as a brute fact (axiom), as this would make the machine unsound and inconsistant. I sometimes, when I want to be short, refer to a machine theology by describing it by the label Tarski minus Gödel, that is the truth on the machine minus what the machine can prove. Incompleteness means that it is quite different. Note that Löbian machines can still prove a Truth operator for each of all sentences with a bounded number of quantifier, and can approximate truth in many other ways, which I will not detail here. Tarski theorem is a fundamental component in the unravelling of the machine's theology. See my paper on Plotinus. The reason why the p hypostase, and the Bp p hypostase play the role of the ONE and the SOUL respectively, is that the introspecting machine can discover them despite not being able to give them a name, and so it matches the main defining attribute used for them by the neoplatonist inquirers. Bruno Onward! Stephen -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com . For more options, visit this group at http://groups.google.com/group/everything-list?hl=en . http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
